A variety of weighting procedures have been developed as generalizations of the parametric least-square-curve-fitting process. Hence it seems reasonable to apply weighting methods of nonparametric regression. In March of last year, we published a basic relationship which can be used to estimate the Fourier coefficients of a conditional density in terms of the sample bivariate trigonometric moments ("Trigonometric Maximum Likelihood Estimation and Application to the Analysis of Incomplete Survival Information" JASA 7, 365, P. 132-9). This relationship will enable us to apply our weighting procedures, which up to now have been only applied in the univariate case, to the problem of two-dimensional, nonparametric curve estimation. We intend to continue developing sampling and data abridgement procedures.